Problem: Simplify the following expression: $n = \dfrac{-8r^2 + 8r + 96}{r + 3} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-8$ , so we can rewrite the expression: $ n =\dfrac{-8(r^2 - 1r - 12)}{r + 3} $ Then we factor the remaining polynomial: $r^2 {-1}r {-12} $ ${3} {-4} = {-1}$ ${3} \times {-4} = {-12}$ $ (r + {3}) (r {-4}) $ This gives us a factored expression: $\dfrac{-8(r + {3}) (r {-4})}{r + 3}$ We can divide the numerator and denominator by $(r - 3)$ on condition that $r \neq -3$ Therefore $n = -8(r - 4); r \neq -3$